The present invention is a method and algorithm for image processing.
Interpretation of graphical images from lunar surface photographs to x-ray microscopy is subject to subjective decisions of the interpreter. Efforts have been made to reduce subjectivity through quantified analytical techniques using digitized image data, for example in large-scale remote sensing. Although large-scale remote sensing has been economical having only limited success in the area of automatic lineament identification and mapping.
Radon transform is a much-studied subject in seismic data processing. It relates to Hough transform and xcfx84-xcfx81 transform and slant stack. Both Hough and Radon transform has the ability to transform two-dimensional images with lines into a domain of line parameters where each different line will have a unique peak position. This has led to many recent line detection applications within image processing and computer vision. The following equation is the Radon transform that transforms two dimensional image g(x,y) into xcfx81 and xcex8.             g      ~        ⁡          (              ρ        ,        θ            )        =            ∫              -        ∞            ∞        ⁢                  ∫                  -          ∞                ∞            ⁢                        g          ⁡                      (                          x              ,              y                        )                          ⁢                  δ          ⁡                      (                          ρ              -                              x                ⁢                                  xe2x80x83                                ⁢                cos                ⁢                                  xe2x80x83                                ⁢                θ                            -                              y                ⁢                                  xe2x80x83                                ⁢                sin                ⁢                                  xe2x80x83                                ⁢                θ                                      )                          ⁢                  xe2x80x83                ⁢                  ⅆ          x                ⁢                  xe2x80x83                ⁢                  ⅆ          y                    
When g(x,y) is of typical line characteristics; i.e., g(x,y)= greater than y=a x+b, the transform will have a point appearance in the (xcfx81,xcex8.) plot.
This phenomenon is also seen by its time domain slant stack implementation in seismic data processing where a horizontally layered earth is assumed. This time domain construction is based on the fact that when a plain wave propagates at a certain angle from vertical position, the signal received from a single receiving station will have a unique horizontal phase velocity. If the signal is reflected from a horizontal subsurface layer, the superimposed response received at the recorder should have a plane wave characteristics. Using the reciprocity principle, summation also can be also performed over the receiver axis for a given shot location to decompose the received signal into plain wave energy. This decomposition is the physical basis for slant stack.
The usefulness of the slant stack is to transform the signal from a particular horizontal substrate to a single dot in the transformed domain so that it can be extracted through filtering process where other types of energy can be effectively removed. Imaging seismic signals along its ray path usually defines the energy prorogation direction in general and therefore lends itself to obtaining clear images by this method.
In real images, the lines are not ideal because random noise and signal can overwhelm the true signal. Hence, the resultant transformation becomes difficult to decompose and interpret. The difficulty increases when there are more lines or a combination of short and long lines. This is particularly true when remote sensed imagery, where both man made and nature made line features are prominent and numerous with varying scales and random orientations. The most up-to-date methods for quantifying the linear features from the imagery has little success due to what is called the square pixel problem that introduces the forced regular grid on top of reality.
Imaging by edge detection is well known by several methods including Laplacian Operator Type 1, Laplacian Operator Type 2, Regular High Pass Low Pass Filter, Average Filter, Gaussian Filter, Sobel, Prewitt, Edge Sharpening, Gamma Filter, Mode Filter as well as others. A disadvantage of edge detection techniques is limited resolution or information overloading with a random signal for detailed images.
Hence, there is a need for a method of image processing that can clearly distinguish lines in an irregular pattern.
The present invention is a modified Radon transform. It is similar to the traditional Radon transform for the extraction of line parameters and similar to traditional slant stack for the intensity summation of pixels away from a given pixel, for example ray paths that span a few 10""s of degrees at a given grid in the time and offset domain. However, the present invention differs from these methods in that the intensity and direction of a composite intensity for each pixel are maintained separately instead of combined after the transformation. The ray could span total 360 degree when circular geometry is used. An advantage of this approach is elimination of the work necessary to extract the line parameters (e.g. direction data) in the transformed domain that often is impossible with the traditional approach. The advantage of the modified Radon Transform method is amplified when many lines are present in the imagery or when the lines are just short segments which both occur in actual imagery.